Sunderland are still to identify the man they want to take the club forward as they continue their search for a new manager.
The move comes after Wales failed to qualify for the 2018 World Cup in Russian Federation, a huge disappointed after reaching the semi-finals of Euro 2016.
The FAW have also confirmed Coleman's assistant Kit Symons' resignation.
Former Fulham and Coventry City boss Coleman will team up with Wales internationals Jonny Williams, on loan from Crystal Palace, and right-back Adam Matthews at Sunderland - both of which have played under Coleman at global level.
"But he had a big smile on his face, he's going to an incredible club and I think they'll like his football up there".
West Brom good enough to shock Chelsea - Tony Pulis
Pulis told the media on Friday: "Last year we were one result worse off than we are this year (at this stage)". The 59-year-old is quoted by BBC Sport as saying: "I understand the more you give, the more people want".
Coleman won 38% of his 50 matches in charge of Wales while he guided the nation to their first semi-final of a major global tournament when they reached the last four of the 2016 UEFA European Championship.
"We wish Chris the very best of luck for the future as he returns to club management, a desire for which he has always been honest and open about".
There was speculation that Northern Ireland boss Michael O'Neill had turned down an opportunity to manage the club and Barnsley's Paul Heckingbottom had also been heavily linked with the vacancy.
Previously he had taken charge at Fulham between 2003 and 2007 before stints at Real Sociedad and Coventry City.
Coleman is believed to be giving serious consideration to ending his time at the helm of Wales after he failed to take the Red Dragons to their first World Cup since the 1958 tournament in Sweden. He also had short spells overseas with Spanish club Real Sociedad and Greek side AEL. But he had considered backtracking on that promise before Sunderland persuaded him to head to the north-east.